Discontinuities are encountered when objects collide, when decisions are made, when
switches are turned on or off, when light and sound refract as they pass between different …

We demonstrate a novel response of a nonlinear micromechanical resonator when operated
in a region of strong, nonlinear mode coupling. The system is excited with a single drive …

In this paper, the theory of bifurcations in piecewise smooth flows is critically surveyed. The
focus is on results that hold in arbitrarily (but finitely) many dimensions, highlighting …

Transitions between steady dynamical regimes in diverse applications are often modeled
using discontinuities, but doing so introduces problems of uniqueness. No matter how …

Discontinuous time derivatives are used to model threshold-dependent switching in such
diverse applications as dry friction, electronic control, and biological growth. In a continuous …

Channels with micron-size width have been carved in Y Ba 2 Cu 3 O 7− x (YBCO) coplanar
microwave resonators by micro-collimated swift heavy-ion irradiation at high fluences. The …

This paper presents a general analysis and a concrete example of the catastrophic case of a
discontinuity-induced bifurcation in so-called Filippov nonsmooth dynamical systems. Such …

When a flow suffers a discontinuity in its vector field at some switching surface, the flow can
cross through or slide along the surface. Sliding along the switching surface can be …

At a two-fold singularity, the velocity vector of a flow switches discontinuously across a
codimension one switching manifold, between two directions that both lie tangent to the …

In this paper we provide a full topological and ergodic description of the dynamics of Filippov
systems nearby a sliding Shilnikov orbit Γ Γ. More specifically we prove that the first return …